• Corpus ID: 247058871

The Boolean complexity of computing Chow forms

@article{Dogan2022TheBC,
  title={The Boolean complexity of computing Chow forms},
  author={Mahmut Levent Dogan and Alperen Ali Erg{\"u}r and Elias P. Tsigaridas},
  journal={ArXiv},
  year={2022},
  volume={abs/2202.11582}
}
We consider the complexity of computing Chow forms and their generalization to multiprojective spaces. We develop a deterministic algorithm using resultants, and obtain a single exponential complexity upper bound. Earlier computational results for Chow forms were in the arithmetic complexity model; our result represents the first Boolean complexity bound. We also extend our algorithm to multiprojective Chow forms and obtain the first computational result in this setting. The motivation for our… 
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References

SHOWING 1-10 OF 37 REFERENCES
Computing Chow Forms and Some Applications
We prove the existence of an algorithm that, from a finite set of polynomials defining an algebraic projective variety, computes the Chow form of its equidimensional component of the greatest…
Randomized and deterministic algorithms for the dimension of algebraic varieties
  • P. Koiran
  • Computer Science, Mathematics
    Proceedings 38th Annual Symposium on Foundations of Computer Science
  • 1997
TLDR
This work shows that the problem of computing the dimension of algebraic varieties is NP-complete in the Blum-Shub-Smale model of computation over C, that it admits a s/sup O(1)/D/Sup O(n)/ deterministic algorithm, and that for systems with integer coefficients it is in the Arthur-Merlin class under the Generalized Riemann Hypothesis.
How to compute the Chow form of an unmixed polynomial ideal in single exponential time
  • Leandro Caniglia
  • Mathematics, Computer Science
    Applicable Algebra in Engineering, Communication and Computing
  • 2005
TLDR
Anefficiently parallelizable single exponential time algorithm which computes the Chow form of the idealI:= (F1,⋯, Fm), provided that I is unmixed, requires only linear algebra computations overK.
The Computational Complexity of the Chow Form
TLDR
A bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety that improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms.
Geometry And Combinatorics Of Chow Forms
The Chow form of a variety is similar to a resultant. Given d + 1 linear forms on a d-dimensional projective variety, the Chow form is a polynomial in the coeecients of the linear forms (unique up to…
Polynomial-Time Computation of the Dimension of Algebraic Varieties in Zero-Characteristic
  • A. Chistov
  • Mathematics, Computer Science
    J. Symb. Comput.
  • 1996
TLDR
An algorithm is described for the computation of the dimension of a projective algebraic variety over a zero characteristic ground field and the working time is polynomial in the size of input and d n.
The Multivariate Schwartz-Zippel Lemma
We show that, except for a special family of polynomials -that we call $\lambda$-reducible-, a natural multivariate generalization of Schwartz-Zippel-DeMillo-Lipton lemma holds. Moreover, we develop…
Introduction to Chow Forms
This article gives an elementary introduction to the theory of Chow forms. It is based on a sequence of four lectures given at the conference on “Invariant Methods in Discrete and Computational…
The Hurwitz form of a projective variety
Multigraded Cayley-Chow forms
...
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